This manga takes a romanticized but inverted view of tribal life. In real nomadic tribes, ALL the life-sustaining work is done by the women. They tend to the livestock, find and obtain water, forage for daily food (wild cereals and root vegetables), make the textile and household items (including the tents), and manage the resources in general. The men help with herding, which mainly involves walking (or riding if it's an equestrian tribe) around with a whip and just watching the flock, and they occasionally help with work that require some muscle. Most nomadic tribal livestock are natural herd animals, so they basically herd themselves, and once the camp is set up there is little for the men to do besides herding the livestock. They occasionally hunt, but most women can hunt just as well. In fact, in most tribal societies the women do more of the hunting than the men. Daily hunting is done with a combination of traps and light projectiles that require little muscle power to use. Seasonal or annual hunting is done by mass herding of large animals by the entire tribe. Men are actually of little use in the daily life of the tribe and serve a secondary function in securing livelihood. Golden Kamuy shows this perfectly.
Men's real job in the tribe is to fight. The biggest threat to nomadic tribes is other humans, both nomadic and settled. Nomads need large swathes of land to graze their livestock, so they need to protect and take land all the time. That's why all their men must be able to fight. That's also why men's bows in nomadic tribal societies are invariably warbows; draw weights over 60 lbs. This is not needed for any kind of hunting where the target is not able to shoot back.
A side note here, but there is this myth in the US that the First Nations sold land because they didn't understand that land could be owned. That's poppycock. All tribal societies place great value on ownership of land. Plains Indians had direct relationships with settled nations in what is now Mexico, and those guys not only held land, they built fortresses. What the First Nations couldn't understand was that it was possible for small numbers of distributed settlers living outside walled cities to rely on an unseen standing military to defend them. Nomads defend their own and use their own to take others' lands. The idea that a faraway group of men totally dedicated to warfare would be willing to protect scattered farmers was alien to them. This was also the exact same problem North Asian tribes faced when the first armies of the Zhou started marching into their lands, although in their case they had time to consolidate into great khanates able to organize an effective resistance and later conquest of their settled neighbors.
This is where another misconception comes into this manga. Nomadic societies place great value on physical beauty of both men and women. Men's real job is to fight, so handsome men are sought after because they tend to be charismatic and charismatic men can easily draw followers. We see this a lot in modern societies as well, including in manga where riajuu are always moving in flocks. Well, translate that into a nomad society and you get the handsome and fit boys riding around in warbands driven by charismatic leaders. If you're a young woman married to a handsome boy you have a better chance to end up as the wealthy wife of a powerful warlord down the line, especially during times of external threat when everyone wanted to consolidate to offer effective resistance. Otoyomegatari encapsulates all the nomadic values perfectly when it presents Amir's brothers as total hotties. THEY HAVE TO BE, in order to hold their position in tribal society.
I live in Indonesia where these tribal values are a big problem in islands outside of Java. Four, maybe three generations ago, many tribes still fought each other regularly and all the men ever did was fight. The women did all the work. Back then it was fair because they did need the men to fend off real threats. Nowadays there's the police to settle disputes and if tribes go to war the army would come to stop them, so the men are effectively unemployed. Yet they still insist on behaving like they're still warriors like in the old days. They spend their lives lounging around smoking and drinking and cockfighting. Sometimes they organize hunting parties, but boar meat doesn't sell for much in mostly-Muslim Indonesia, and the deer are protected by law. So the women suffer and the men waste away their lives. There are ongoing efforts to fix the situation with education and training, but change will take a very long time.
So what about the values of masculinity described in this manga? Well, they are ironically those of settled peasants. Peasants generally don't care about looks because in peasant societies men do carry the burden of the work. Farming is mostly a man's job, and women generally tend to the house and serve the needs of the men. That's why physical strength and diligence is sought after in men and good cooking skills are sought after in women. Looks don't last in a peasant society where harsh living conditions very quickly erode any sign of youthfulness.